Problem: Umaima is 2 times as old as Ishaan. Twelve years ago, Umaima was 6 times as old as Ishaan. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Umaima and Ishaan. Let Umaima's current age be $u$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $u = 2i$ Twelve years ago, Umaima was $u - 12$ years old, and Ishaan was $i - 12$ years old. The information in the second sentence can be expressed in the following equation: $u - 12 = 6(i - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $u$ and substitute it into our second equation. Our first equation is: $u = 2i$ . Substituting this into our second equation, we get: $2i$ $-$ $12 = 6(i - 12)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $2 i - 12 = 6 i - 72$ Solving for $i$ , we get: $4 i = 60.$ $i = 15$.